Question

Question 12

Prove that a cyclic parallelogram is a rectangle.

Solution

Let ABCD be a cyclic parallelogram.

∠A+∠C=180∘ (Opposite angles of a cyclic quadrilateral)

We know that opposite angles of a parallelogram are equal.

∴∠A=∠C and ∠B=∠D

∠A+∠C=180∘

Then ∠A+∠A=180∘

∴2∠A=180∘

⇒∠A=∠C=90∘

Parallelogram ABCD has one of its interior angles as 90∘. Therefore, it is a rectangle.

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